The protections were first introduced in March, and in June they were extended until the end of September to bring the state into line with the expiry of protections in other states and territories.

Tenants' Union of Tasmania acting principal solicitor Ben Bartl called on the Premier to extend the moratorium until the end of the year as had recently occurred in Victoria.

"The current protections have guaranteed a safe haven at a time when all the medical evidence recommends that people stay home," Mr Bartl said.

"A failure to extend the protections for residential tenants may result in an avalanche of eviction orders as landlords attempt to evict tenants or raise rents for tenants who are already in financial stress.

"It will result in evictions for people who through no fault of their own have lost their jobs and are struggling to pay the rent."

Greens leader and housing spokeswoman Cassy O'Connor said her party had written to the Premier earlier this month urging him to keep the rental protections in place but regrettably they were yet to receive a response.

"The looming deadline is frightening and extremely stressful for many people, who are relying on support payments and rental protections," Ms O'Connor said.

"The Premier needs to act now to extend rental protections and provide private rental tenants peace of mind.

"Landlords should also be given plenty of forewarning to ensure tenants aren't coerced in to signing new lease or rental agreements before the September 30 deadline."

Ms O'Connor said she had been hearing stories of landlords threatening tenants with a choice of eviction or increased rent.

"This is likely to escalate as we approach the end of September," she said.

Labor housing spokeswoman Alison Standen said the government should ensure the protections remained in place until December 1 when it is expected the state's border restrictions will be eased.

"It's not too early to consider the level of hardship that tenants, both commercial and residential, will continue to experience in light of the border lockdown and the uncertainty and impact on jobs and income support provided by way of JobSeeker and JobKeeper," Ms Standen said.

"It would be disastrous for tenants already facing financial hardship to be hit with the double whammy of reduced income at the same time as suffering higher costs for keeping a roof over their head

"Both tenants and landlords would benefit from the certainty this would provide."

Building and Construction Minister Elise Archer said the government was closely monitoring the economic situation and would make a decision regarding the expiry of the protections well before the end of September.

"The Tasmanian government acted quickly to protect and support residential tenants at risk of eviction as a result of the impacts of COVID-19," Ms Archer said.

"These protections have enabled Tasmanian tenants to stay in their homes as they dealt with the economic uncertainty associated with the COVID-19 pandemic."